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Abstract

We present numerical experiments showing how coupled-mode theory can be systematically applied to join very dissimilar photonic crystal waveguides with 100% transmission. Our approach relies on appropriately tuning the coupling of the evanescent tail of a cavity mode to each waveguide. The transition region between the waveguides may be as short as a few lattice spacings. Moreover, this technique only requires varying a small number of parameters (two for each waveguide in our example) and the tuning to each waveguide may be done separately, greatly simplifying the computations involved.

Figures (4)

Projected band diagram along the Γ – X direction for TM modes in a square lattice of rods of radius a/4 (shaded region) and band structures for a singly-wide line defect, triply-wide line defect, and coupled-cavity waveguide (identified by their dielectric profile). The defect radii are, respectively, a/12, 0.325a, and a/12. The constant Λ (x–axis of the figure) is 4 for the CCW and 1 for the other structures, due to the longer primitive cell (4a) of the former, along the direction of the propagation.

Graphical representation of a coupled-mode theory treatment of two waveguides (red and blue strips) coupled by means of a cavity tuned to resonate at the angular frequency ω0 and couple to each waveguide with quality factors Q1 and Q2. The direct coupling between the two waveguides is neglected. 100% transmission occurs at the frequency ω0 when Q1 = Q2.

Results of a finite-difference time-domain (FDTD) simulation of a cavity resonant at ω0 = 0.265 × (2πc/a) decaying into a singly-wide line defect waveguide (a), a triply-wide line defect waveguide (b), and a slow-light coupled-cavity waveguide (c). The top panels show the z component (parallel to the rods) of the electric field. The insets show the dielectric profile of the area indicated. The lower panels show the dependence of the cavity Q on the defect radius of the rod closest to the waveguide (insets, in red). The latter are tuned so that the Q of the cavity is 550 in each case. The values of the defect radii indicated in blue are used in the full simulations of the coupled waveguides.

FDTD simulations showing the z component of the electric field (top panels) and the transmission spectrum of a singly-wide line defect waveguide coupling to triply-wide waveguide (a), a singly-wide waveguide coupling to a CCW (b), and a triply-wide waveguide coupling to a CCW (c). Each system is tuned to the points indicated (in blue) in Fig. 3 and exhibits 100% transmission near ω0 = 0.265 × (2πc/a). For reference, the transmission spectra of the corresponding butt-coupled geometries are shown as dash-dotted lines.